St. Peter’s basilica

The earlier in the day, the better. No, it’s free to visit. There’s a security checkpoint that everyone must pass through and it pretty much always has a line.

Welcome to the forum!
As above, no there is no fee.
There is a special entrance for disabled visitors but it appears to be for wheelchairs; I'm not sure persons using canes for support will be allowed to use it nor can I find any mention of any being allowed to do so...although it's possible I've missed those. That said, you could contact the office via the link provided with your question?
https://www.basilicasanpietro.va/en/experience-the-basilica/services-for-people-with-disaabilities.html

But Is your aunt a Catholic whose main interest in the basilica is for prayer and spiritual reflection? If so, this information regarding a special "Prayer Path" for the faithful - with entry through a special gate - may be of interest:

https://www.basilicasanpietro.va/en/experience-the-basilica/services-for-pilgrims/access-for-pilgrims.html
https://www.basilicasanpietro.va/en/experience-the-basilica/services-for-pilgrims/info-and-reception.html

Not that you have ANY intention of doing so but if her main interest in visiting the basilica is not for prayer or pilgrimage, I'd leave use of the "Prayer Path" to those there for those specific reasons. This special service is noted as ad experimentum - temporary or experimental - and too many using it just to gain entry more quickly may result in cancellation of the program. :O)

Editing to add: if your visit is during Jubilee 2025, visits to St Peter's will likely involve larger crowds than usual and working around special masses/services.
https://www.iubilaeum2025.va/en.html
https://www.usccb.org/committees/jubilee-2025